Systems of equations word problems in high school Algebra

Question

I'm not sure how to set up the equations to solve a problem like:

Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of plane in still air.

Answer 1

If you call $v_p$ the speed of the plane and $v_w$ the speed of the wind then

$$v_p+v_w=158\\ v_p-v_w=112$$

Now solve the system.

Answer 2

Let W and P be the speeds of the wind and the plane respectively. Then you have that $$W+P=158$$ and $$P-W=112$$ Adding the two equations gives $$2P=270$$ or $$P = 135$$ so $$W=23$$

Answer 3

Flying to Kampala with a tailwind a plane averaged 158 km/h.

$$ v + w = 158 $$

On the return trip the plane only averaged 112 km/h while flying back into the same wind.

$$ v - w = 112 $$

Find the speed of the wind and the speed of plane in still air.

The linear system has been stated, now solve for $v$ and $w$.